Steve,
Czorny just reminded me that I forgot to tell you that each Eiso s2233W monitor has his own LUT. So if I understand correctly, I don't even need a dual head video card?!
This would be correct though I'm not familiar with this monitor. If it has its own internal hardware LUT AND you're using the proper software which is designed to access these LUT's then you should be able to get this to work with your current video card PROVIDING .. well.. a lot.. I'll run through a few things. I've been running dual monitors side by side (identical models.. I'm now running two NEC LCD2690uxi2's..) for over ten years on various versions of Windows so it can indeed be done. This is what I do..
1. Uninstall anything but the base driver. Go to msconfig.sys and your startup tray and disable anything from Nvidia but the base driver. This is to start. Later you can enable the extra stuff (the programs that enable you to adjust brightneess/color/contrast/etc) if you wish and see what if anything is causing an issue.
2. Totally clear all current profiles from the Windows Color Management applet. You'll find this under the Control Panel. Yes, I know the color profile program should replace these.. but I've discovered funny things can happen which shouldn't during this exchange. Start with a blank slate for both monitors. Also go to windows/system32/spool/drivers/color and delete all your old profiles.
3. Unplug your LAN cable or wireless card from the internet.
4. Disable your virus checker or malware programs if any.
5. Reboot, ensure you're running on the base video card driver only with no extras, the color manager is clear, and that your virus checkers are disabled.
6. Run the color profiler software Eizo recommends to access the internal hardware LUT's for these monitors.. and follow their directions exactly. Make sure the 1i2 is firmly but not pressed on the screen. Either tilt your screens back so gravity does this.. or I personally use my back scratcher to lean on it.. ;o)
This is a start.. now.. Even with two like monitors there WILL be some white point variances between the two monitors which will be visible if you span a white background box across both monitors.. you'll find the colors and grays will look fine (if you did it right) but the whites can be off which is inconsequential.. but irritating. NEC SVII provides a means to correct this small difference by eye.. and it works as advertised in every mode but sRGB Emulation.. an issue I'll be contacting NEC about this week as I'm just now setting my new 2690's..
Now.. you're going to find some weird differences attributed to Windows and Windows programs. For instance.. some applications will pick up the proper profile if you drag the application from one monitor to the other.. others won't. You'll need to learn which are which. Just know that when it happens it's not necessarily an issue with your color setup. Windows Explorer on the second monitor.. if displaying thumbnails and if you're using a wide gamut monitor.. might display those thumbnails with a very high saturated look.. but when you click on them and bring them up in your viewer of choice they'll be fine (provided your viewer of choice is color aware).. so don't worry about it..
There's a bucket load of other small issues and discrepancies when using two monitors.. once you get past the LUT issue you'll discover these. But over all when processing images in the main image programs you'll be fine.
I'm using dual ATI 5770 cards and use one per monitor even though each card supposedly handles 3 LUT's.. and even though the monitors have internal LUT's and I'm using them via SVII. I do this because I get less issues with the smaller stuff.. and because I also run a 1080p 50" HDTV for soft proofing with clients.. and yes a HDTV properly profiled can (providing its a quality unit) can display exact colors.. but how you color profile a HDTV depends on which input you're using and for what purpose.. each input (HDMI for PC, HDMI for media player box, HDMI for Blue-ray, cable box, etc, etc) needs to be separately adjusted and in different ways using different gear.. but thats another story..
Good luck.